Inverse problem of recovering a time-dependent nonlinearity appearing in third-order nonlinear acoustic equations

Abstract

Abstract This paper is concerned with the inverse problem of recovering the nonlinearity for Jordan-Moore-Gibson-Thompson equations (J-M-G-T equations for short), which is a third order nonlinear acoustic equation. The well-posedness of the nonlinear equation is obtained for the small initial and boundary data. By the second order linearization to the nonlinear equation, and the construction of complex geometric optics (CGO) solutions for the linearized equation, the uniqueness of recovering the nonlinearity is derived.